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Igoe M, Casagrandi R, Gatto M, Hoover CM, Mari L, Ngonghala CN, Remais JV, Sanchirico JN, Sokolow SH, Lenhart S, de Leo G. Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries. Bull Math Biol 2023; 85:31. [PMID: 36907932 PMCID: PMC10008208 DOI: 10.1007/s11538-023-01137-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 02/20/2023] [Indexed: 03/14/2023]
Abstract
Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.
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Affiliation(s)
- Morganne Igoe
- Department of Mathematics, University of Tennessee, Knoxville, TN, USA.
| | - Renato Casagrandi
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | - Marino Gatto
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | - Christopher M Hoover
- Division of Environmental Health Sciences, University of California, Berkeley, Berkeley, CA, USA
| | - Lorenzo Mari
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | | | - Justin V Remais
- Division of Environmental Health Sciences, University of California, Berkeley, Berkeley, CA, USA
| | - James N Sanchirico
- Environmental Science and Policy, University of California, Davis, Davis, CA, USA
| | - Susanne H Sokolow
- Stanford Program for Diseases Ecology, Health and the Environment, Stanford University, Pacific Grove, CA, USA
| | - Suzanne Lenhart
- Department of Mathematics, University of Tennessee, Knoxville, TN, USA
| | - Giulio de Leo
- Department of Earth System Science and Department of Oceans, Hopkins Marine Station, Stanford Doerr School of Sustainability, Stanford University, Pacific Grove, CA, USA
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Sisk A, Fefferman N. A network theoretic method for the basic reproductive number for infectious diseases. Methods Ecol Evol 2022. [DOI: 10.1111/2041-210x.13978] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Anna Sisk
- Department of Mathematics University of Tennessee Knoxville Tennessee USA
| | - Nina Fefferman
- Department of Mathematics University of Tennessee Knoxville Tennessee USA
- Department of Ecology & Evolutionary Biology University of Tennessee Knoxville Tennessee USA
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Angina J, Bachhu A, Talati E, Talati R, Rychtář J, Taylor D. Game-Theoretical Model of the Voluntary Use of Insect Repellents to Prevent Zika Fever. DYNAMIC GAMES AND APPLICATIONS 2022; 12:133-146. [PMID: 35127230 PMCID: PMC8800840 DOI: 10.1007/s13235-021-00418-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/10/2021] [Indexed: 05/14/2023]
Abstract
Zika fever is an emerging mosquito-borne disease. While it often causes no or only mild symptoms that are similar to dengue fever, Zika virus can spread from a pregnant woman to her baby and cause severe birth defects. There is no specific treatment or vaccine, but the disease can be mitigated by using several control strategies, generally focusing on the reduction in mosquitoes or mosquito bites. In this paper, we model Zika virus transmission and incorporate a game-theoretical approach to study a repeated population game of DEET usage to prevent insect bites. We show that the optimal use effectively leads to disease elimination. This result is robust and not significantly dependent on the cost of the insect repellents.
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Affiliation(s)
- Jabili Angina
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Anish Bachhu
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Eesha Talati
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Rishi Talati
- Department of Biology, Virginia Commonwealth University, Richmond, VA 23284-2012 USA
| | - Jan Rychtář
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 USA
| | - Dewey Taylor
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 USA
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Garzón DN, Castillo Y, Navas-Zuloaga MG, Darwin L, Hardin A, Culik N, Yang A, Castillo-Garsow C, Ríos-Soto K, Arriola L, Ghosh A. Dynamics of prion proliferation under combined treatment of pharmacological chaperones and interferons. J Theor Biol 2021; 527:110797. [PMID: 34090904 DOI: 10.1016/j.jtbi.2021.110797] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Revised: 05/20/2021] [Accepted: 05/31/2021] [Indexed: 11/15/2022]
Abstract
Prions are proteins that cause fatal neurodegenerative diseases. The misfolded conformation adopted by prions can be transmitted to other normally folded proteins. Therapeutics to stop prion proliferation have been studied experimentally; however, it is not clear how the combination of different types of treatments can decrease the growth rate of prions in the brain. In this article, we combine the implementation of pharmacological chaperones and interferons to develop a novel model using a non-linear system of ordinary differential equations and study the quantitative effects of these two treatments on the growth rate of prions. This study aims to identify how the two treatments affect prion proliferation, both individually and in tandem. We analyze the model, and qualitative global results on the disease-free and disease equilibria are proved analytically. Numerical simulations, using parameter values from in vivo experiments that provide a pharmaceutically important demonstration of the effects of these two treatments, are presented here. This mathematical model can be used to identify and optimize the best combination of the treatments within their safe ranges.
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Affiliation(s)
| | | | | | | | | | | | - Anji Yang
- University of Shanghai for Science and Technology, China
| | | | | | - Leon Arriola
- Department of Mathematics, University of Wisconsin Whitewater, Whitewater, WI 53190, USA
| | - Aditi Ghosh
- Department of Mathematics, University of Wisconsin Whitewater, Whitewater, WI 53190, USA.
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Counotte MJ, Althaus CL, Low N, Riou J. Impact of age-specific immunity on the timing and burden of the next Zika virus outbreak. PLoS Negl Trop Dis 2019; 13:e0007978. [PMID: 31877200 PMCID: PMC6948816 DOI: 10.1371/journal.pntd.0007978] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Revised: 01/08/2020] [Accepted: 12/08/2019] [Indexed: 01/27/2023] Open
Abstract
The 2015-2017 epidemics of Zika virus (ZIKV) in the Americas caused widespread infection, followed by protective immunity. The timing and burden of the next Zika virus outbreak remains unclear. We used an agent-based model to simulate the dynamics of age-specific immunity to ZIKV, and predict the future age-specific risk using data from Managua, Nicaragua. We also investigated the potential impact of a ZIKV vaccine. Assuming lifelong immunity, the risk of a ZIKV outbreak will remain low until 2035 and rise above 50% in 2047. The imbalance in age-specific immunity implies that people in the 15-29 age range will be at highest risk of infection during the next ZIKV outbreak, increasing the expected number of congenital abnormalities. ZIKV vaccine development and licensure are urgent to attain the maximum benefit in reducing the population-level risk of infection and the risk of adverse congenital outcomes. This urgency increases if immunity is not lifelong.
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Affiliation(s)
- Michel J. Counotte
- Institute of Social and Preventive Medicine, University of Bern, Bern, Switzerland
- Graduate School for Cellular and Biomedical Sciences, University of Bern, Bern, Switzerland
| | - Christian L. Althaus
- Institute of Social and Preventive Medicine, University of Bern, Bern, Switzerland
| | - Nicola Low
- Institute of Social and Preventive Medicine, University of Bern, Bern, Switzerland
| | - Julien Riou
- Institute of Social and Preventive Medicine, University of Bern, Bern, Switzerland
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Miyaoka TY, Lenhart S, Meyer JFCA. Optimal control of vaccination in a vector-borne reaction-diffusion model applied to Zika virus. J Math Biol 2019; 79:1077-1104. [PMID: 31187254 DOI: 10.1007/s00285-019-01390-z] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Revised: 05/22/2019] [Indexed: 12/14/2022]
Abstract
Zika virus has acquired worldwide concern after a recent outbreak in Latin America that started in Brazil, with associated neurological conditions such as microcephaly in newborns from infected mothers. The virus is transmitted mainly by Aedes aegypti mosquitoes, but direct (sexual) transmission has been documented. We formulate a reaction diffusion model that considers spatial movement of humans and vectors, with local contact transmission of Zika virus. Vaccination is introduced as a control variable, giving immunity to susceptible humans, in order to characterize an optimal vaccination strategy that minimizes the costs associated with infections and vaccines. The optimal control characterization is obtained in terms of state and adjoint equations. Parameter estimation and numerical simulations are carried out using data for the initial 2015 Zika outbreak in the state of Rio Grande do Norte in Brazil. Several scenarios are considered and analyzed in terms of number of new infections and costs, showing that the optimal control application is successful, significantly reducing these quantities.
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Affiliation(s)
- Tiago Yuzo Miyaoka
- Department of Applied Mathematics, IMECC, University of Campinas, Campinas, SP, Brazil.
| | - Suzanne Lenhart
- Department of Mathematics, University of Tennessee, Knoxville, TN, USA
| | - João F C A Meyer
- Department of Applied Mathematics, IMECC, University of Campinas, Campinas, SP, Brazil
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